The half-life for the second-order reaction of a substance A is 58.2 s when A0 = 0.63 mol L-1 Calculate the time needed for the concentration of A to decrease to the following values.
(a) one-third of its original value
(b) one-sixth of its original value
(c) one-seventh of its original value
What's wrong with substituting values into the second order equation and solving for time.
Could it be you don't know how to handle 1/3, 1/6, 1/7 th values?
If Ao = 0.63 then 1/3 that = ? for a; 1/6 that for b and 1/7 that for c.
I don't understand how to figure out K.
I used the information in the problem given to solve for k, and then plug that k in to solve for t, but it's not the correct answer.
t1/2 = [1/k(Ao)]
I understand, but what is K or how can I determine K?
The problem GIVES you the half life. Use that and the equation I provided above to determine k.
To calculate the time needed for the concentration of substance A to decrease to the given values, we need to use the integrated rate equation for a second-order reaction:
1/[A] = kt + 1/[A]₀
Where:
[A] is the concentration of substance A at a certain time (t)
[A]₀ is the initial concentration of substance A
k is the rate constant
t is the time
Let's start by finding the rate constant (k) using the given half-life.
Step 1: Finding the rate constant (k)
Half-life (t₁/₂) for a second-order reaction is given by the formula:
t₁/₂ = 1 / (k[A]₀)
Rearranging the formula to solve for k:
k = 1 / (t₁/₂⋅[A]₀)
Substituting the given values:
t₁/₂ = 58.2 s
[A]₀ = 0.63 mol L⁻¹
k = 1 / (58.2 s ⋅ 0.63 mol L⁻¹)
Now that we have the rate constant, we can proceed to calculate the time needed for the concentration of A to decrease to the desired values.
(a) To find the time needed for the concentration to decrease to one-third of its original value:
1/[A] = kt + 1/[A]₀
1 / (1/3⋅[A]₀) = k⋅t + 1/[A]₀
Simplifying the equation:
3 / [A]₀ = k⋅t + 1/[A]₀
Rearranging the equation to solve for t:
k⋅t = 3 / [A]₀ - 1/[A]₀
t = (2 / [A]₀) / k
Substituting the known values:
t = (2 / 0.63 mol L⁻¹) / k
Calculate t using the previously determined value of k.
(b) Repeat the same process to calculate the time needed for the concentration to decrease to one-sixth of its original value.
Substituting the known values into the equation:
t = (5 / 0.63 mol L⁻¹) / k
(c) Repeat the same process to calculate the time needed for the concentration to decrease to one-seventh of its original value.
Substituting the known values into the equation:
t = (6 / 0.63 mol L⁻¹) / k
Calculate t using the previously determined value of k.
By following these steps and substituting the given values into the equations, you will be able to find the time needed for the concentration of substance A to decrease to the desired values.